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Let A(2, -3) and B(-2, 1) be two vertices of a triangle. If the third vertex is allowed to move along the line 2x + 3y = 9, then the path traced by the centroid of the triangle is:

1. x - y = 1
2. 2x + 3y = 1
3. 2x + 3y = 3
4. 2x - 3y = 1

Correct answer: 2x + 3y = 1

Solution

The centroid of a triangle is the average of the coordinates of its vertices. As the third vertex moves along the line 2x + 3y = 9, the centroid's coordinates can be expressed as a linear combination of the fixed vertices A and B, leading to the equation 2x + 3y = 1.

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